In repeated games with differential information on one side, the labelling "general case" refers to games in which the action of the informed player is not known to the uninformed, who can only observe a signal which is the random outcome of his and his opponent's action. Here we consider the problem of minimizing regret (in the sense first formulated by J. Hannan (1956, in Contributions to the Theory of Games, Vol. III, Annals of Mathematics Studies, Vol. 39, Princeton, NJ: Princeton Univ. Press.) when the information available is of this type. We give a simple condition describing the approachable set. Journal of Economic Literature Classification Number: D81, D82, D83.
Bibliographical noteFunding Information:
* The author thanks Jean-Fran¸cois Mertens for illuminating conversations. I tried to make the most of them, but the mistakes are my responsibility. I also thank Rakesh Vohra, for his competent and friendly help; and two referees for their extremely helpful comments, and for their patience. They forced me to try and make this paper intelligible. Any remaining shortcomings are my responsibility. Finally I thank the NSF for financial support of this research.
- Differential information
- Minimize regret